Multiscale Curvature Detection in Computer Vision

This thesis presents a new method for detection of complex curvatures such as corners, circles, and star patterns. The method is based on a second degree local polynomial model applied to a local orientation description in double angle representation. The theory of rotational symmetries is used to compute curvature responses from the parameters of the polynomial model. The responses are made more selective using a scheme of inhibition between different symmetry models. These symmetries can serve as feature points at a high abstraction level for use in hierarchical matching structures for 3D estimation, object recognition, image database search, etc. A very efficient approximative algorithm for single and multiscale polynomial expansion is developed, which is used for detection of the complex curvatures in one or several scales. The algorithm is based on the simple observation that polynomial functions multiplied with a Gaussian function can be described in terms of partial derivatives of the Gaussian. The approximative polynomial expansion algorithm is evaluated in an experiment to estimate local orientation on 3D data, and the performance is comparable to previously tested algorithms which are more computationally expensive. The curvature algorithm is demonstrated on natural images and in an object recognition experiment. Phase histograms based on the curvature features are developed and shown to be useful as an alternative compact image representation. The importance of curvature is furthermore motivated by reviewing examples from biological and perceptual studies. The usefulness of local orientation information to detect curvature is also motivated by an experiment about learning a corner detector.